Optimal Control Problem for a Modified Novikov Equation with Dissipation
Jiangbo Zhou *
Department of Mathematics, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China.
Jing Chen
Department of Mathematics, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China.
Junde Chen
Department of Mathematics, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China.
*Author to whom correspondence should be addressed.
Abstract
This paper investigate the optimal control problem for a modified Novikov equation with dissipation. The existence and uniqueness of regular local solution to the corresponding initial boundary value problem is guaranteed by the Faedo-Galerkin method. A critical estimate of the solution is obtained. Finally, the existence of an optimal solution to the control problem is proved.
Keywords: Modified Novikov equation, optimal control, weak solution